The Global Positioning System (GPS) allows any one equipped with a suitable receiver to read off his or her position anywhere in the world to within an inch or two. The system is based on the normally-correct assumption that each of its 24 satellites knows exactly where it is in space at any instant.
Moreover, each satellite transmits radio pulses at precisely predetermined times so a receiver on the ground with an accurate clock can calculate how long it takes each pulse to reach it.
Since the speed of the signal is known, elementary algebra provides the distance of the receiver from the satellite, and simultaneous readings from several different spacecraft allow the receiver to pinpoint its position on the surface of the Earth.
Meteorologists have found ways to use the GPS for weather forecasting.
It is known, for example, that water vapour in the Earth's atmosphere delays the radio signals very slightly. Normally this potential error is corrected for but some meteorologist somewhere had the bright idea of not correcting for the moisture; a GPS receiver on the ground used in this fashion will therefore read a position that is false by several centimetres.
The size of the error is a measure of the amount of water vapour in the atmosphere, and since the receiver's true location is already known, the error can be identified exactly.
A network of GPS receivers used in this way can be used to calculate the "precipitable water vapour", or what might be called "the potential amount of rain", over a large area.
And then they discovered that the GPS could measure temperature.
Radio waves are also bent, or refracted, by the atmosphere from the original straight-line path along which they began their journey towards the Earth. The amount of refraction is proportional to the average temperature of the air through which the signal passes.
Now think of a second satellite "listening" for the GP, and imagine it picking up a signal from a GPS spacecraft positioned such that its radio waves have to travel tangentially through the atmosphere to get to its receiver: the signal just misses our planet, skims through the upper atmosphere, and emerges into space again to the receiving satellite. Such a signal will be refracted during its brief sojourn through the air and, consequently, the receiver will compute a false position for the GPS transmitter.
But again we know where the GPS satellite really is and the difference between its computed and its true location is a measure of the temperature of the upper atmosphere through which the signal passes.